Application of an extended Kalman filter in a feedback control of a generalized nonlinear bacterial growth system

In previous work by T.W. Wang et al. (1987) the robust multivariable linear quadratic Gaussian/loop transfer recovery (LQG/LTR) control design methodology was used in designing for the control of the linearized version of a generalized nonlinear bacterial growth system. Here, the effect of applying an extended Kalman filter (EKF) in conjunction with the same linear feedback regulator in the control of similarly modeled continuous generalized nonlinear bacterial growth system is investigated. Presented results show that: (1) the tracking ability of the EKF system is improved in the absence of plant-model mismatch; and (2) in the presence of the same set of perturbations, the closed EKF loop system is again maintained stable, provided the same values of noise covariances are used as those in the previous LQG/LTR design. However, if the relative ratio of the process and measurement noise covariances is changed, then the same set of perturbation can destabilize the closed system. The robustness property of the EKF closed-loop system depends partly on the choice of the noise covariances. The proper tuning of the EKF by selecting an appropriate set of noise covariances to yield a robust final control design is addressed, but is not resolved